A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?

The correct option is (b) - 30% increase.

Solution

Let the initial monthly salary of the person be 100 units.
Initial Savings = 10% of 100 = 10 units.
Initial Expenditure = Salary - Savings = $100-10=90$ units.

New Scenario:
New Salary = Initial Salary + 12% increase = $100+12=112$ units.
New Expenditure = Initial Expenditure + 10% increase = 90 + (10% of 90) = $90+9=99$ units.

Calculating New Savings:
New Savings = New Salary - New Expenditure
New Savings = $112-99=13$ units.

Calculating Percentage Change in Savings:
Change in Savings = New Savings - Initial Savings = $13-10=3$ units.
Percentage Change = (Change / Initial Savings) * 100
Percentage Change = $(3/10)\times 100=30$.

Since the value is positive, it is a 30% increase.

Why the other options are incorrect

• Option (a) - 20% increase: This result would occur if the new savings were 12 units; however, the calculation shows the new savings are 13 units.
• Option (c) - 03% decrease: This is a common error where one might confuse the absolute change (3 units) with a percentage decrease, ignoring that the base value (10) leads to a 30% increase.
• Option (d) - 02% decrease: This might result from incorrectly subtracting the percentage growth of expenditure (10%) from the percentage growth of salary (12%) without accounting for the different base values of salary and expenditure.

Key Concept

The relationship between Salary, Expenditure, and Savings ($S=E+Sav$) where percentage changes must be applied to their respective absolute base values.